# minimalPrimesIP -- one line description if different from minimalPrimesIP

## Synopsis

• Usage:
minimalPrimesIP I
minimalPrimesIP (I, iterations)
• Inputs:
• I, ,
• iterations, an integer, how many iterations of topMinimalPrimesIP should be called
• Outputs:
• a list, the minimal primes of I

## Description

This is basically an alternative version of minimalPrimes.

This function calls topMinimalPrimesIP repeatedly, collecting the primes and passing them in with IgnorePrimes. This is repeated iterations many times or until there are no primes remaining. If iterations is excluded, all minimal primes are returned.

 i1 : R = QQ[x,y,z,w,v]; i2 : I = monomialIdeal(y^12, x*y^3, z*w^3, z*v*y^10, z*x^10, v*z^10, w*v^10, y*v*x*z*w); o2 : MonomialIdeal of R i3 : ScipPrintLevel = 0; i4 : minimalPrimesIP(I, 1) o4 = {monomialIdeal (y, z, v), monomialIdeal (y, z, w)} o4 : List i5 : minimalPrimesIP I o5 = {monomialIdeal (y, z, v), monomialIdeal (y, z, w), monomialIdeal (x, y, ------------------------------------------------------------------------ w, v)} o5 : List i6 : minimalPrimes I o6 = {monomialIdeal (y, z, w), monomialIdeal (y, z, v), monomialIdeal (x, y, ------------------------------------------------------------------------ w, v)} o6 : List

## Caveat

Warning: more than likely, this with take longer than minimalPrimes to return the same output. It some situations topMinimalPrimesIP is much faster than minimalPrimes, but not all.